Punnett squares are useful in genetics to diagram possible genotypes of the offspring of two organisms. The Punnett square for a monohybrid cross tracks the inheritance of a single trait and consists of four boxes, each of which represents a possible genotype. The Punnett square for a dihybrid cross tracks two genes and consists of sixteen boxes.

In Genetics, one of the most useful tools that you'll find is what's known as a punnett square, which is simply a graphical way of helping you figure out genetic problems. Now, once you've seen how to do them, punnett squares are pretty easy. But the key thing to keep in mind is that the gametes of the parents that you're going to be investigating on the outside of the punnett square, while the things inside this punnett square are the offspring. So let me show you an example of a punnett square being used for a cross between two heterozygous individuals and we're going to look at just one gene.

So here's one parent, here's the other. So somebody's big r little r and we're going to do this for the tongue rolling allele versus the recessive non-rolling allele. So this parent, what I do is I know by the first law of Mendel, the law of segregation that these two r's have to separate and wind up in different gametes. So this person can create a gamete that has a big r or they can produce a gamete that has a little r. Alright?

This parent does the same thing. So they produce a gamete that has a big r, they can also produce a gamete that has a little r, alright? To make it more apparent, let me add in some details. So here we have the guy's sperm and the girl's eggs. Alright. So now we make some babies.

So we have a big r big r. A big r combines with the little r getting the point here. We have another big r. Now just as a little technique thing, you always put the dominant allele first even if you think but that one came before. No. You put the dominant one first. And then my last little guy over here is a little r little r. Alright? So I can see that these two parents can produce four offspring. Now one of my offspring is going to be homozygous dominant for a tongue roller. Two of my offspring out of the four possible different offspring will be heterozygous. They can still roll their tongue. So they'll look in a typically the same as this one here. This guy down here is my one homozygous recessive individual, the one non-roller in the group. Alright?

Now this is a great method for predicting offspring but you can also use it for figuring out what the parents are like. For example, let's suppose you get some problem and they give you some numbers. What you want to do is you want to look at those numbers and figure out what's the ratio. And if I get a ratio of 1:1 or 2:2 so half my offspring are one way and roughly half my offspring are another, then what I do is I say let's suppose they tell me half of them can roll their tongue, half cannot. So what I do is I put the offspring into the boxes. Remember this is metaphorical. Don't put babies in boxes.

So I have my little r little r here and a little r little r offspring there. Because I know that half of my offspring can't roll their tongue. Half can. Now I know to not roll your tongue you have to be homozygous recessive. To roll your tongue you have to have at least one dominant big r tongue rolling allele. I don't know what's here though. But this offspring here I see has a little r and a little r. So where did those come from? This first little r must have come from here, alright? This second little r must have come from there. Follow me so far? Great.

So that takes care of let's see, these r's here but where did that little r come from? It didn't come from down there it must have come from here, okay? So now I'm going to this offspring. Now this allele here right now is a bit of a mystery but I do know they have a big r. And that couldn't have come from here so it must come from there. And hey, I figured it out. My parents are big r little r and little r little r. I can then go back if I want to and I can figure out hey those two people who could roll their tongue they were actually heterozygous for that trait. Alright?

So doing a single allele cross or single gene cross like this, pretty simple and pretty easy. It gets a little bit more complicated when you do two genes at once. So let me run through how to do one of the two gene punnett squares. The basic principle is the same. You put the gametes on the outside, offspring in the middle inside of the boxes. So this person can create a big r big e gamete. They can produce a big r little e gamete. Both options are easily probable. Similarly they can do a little r big e and a little r little e. Alright? This parent who happens to have the same genotype for this genes will wind up creating the same possible combination, big r big e, big r little e. Sorry. Little r big e. I was jumping ahead there and little r little e. Alright? So again just like before, I bring the gametes together and I collect similar genes. So the r's go together here, so this portion is big r big r and the e's go together. Big e big e.

Let me skip down to say this person with that gamete. So I have a big r little r. Remember the dominant allele always goes before the recessive and a big e big e. Alright?

Now I could spend a lot of time and fill this up. Let me just skip to the end. This is what it would wind up looking like. And this allows me to create all of my offspring and then I can go through and like you can see here, I color coated all of the different possible phenotypes. And I can say, oh look at this I got my standard 9:3:1 ratio for a cross. So now you know how to do punnett squares. Get at the problems.